English

Trapped Reeb orbits do not imply periodic ones

Symplectic Geometry 2017-08-02 v1 Dynamical Systems

Abstract

We construct a contact form on R^{2n+1}, n at least 2, equal to the standard contact form outside a compact set and defining the standard contact structure on all of R^{2n+1}, which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.

Keywords

Cite

@article{arxiv.1309.4982,
  title  = {Trapped Reeb orbits do not imply periodic ones},
  author = {Hansjörg Geiges and Nena Röttgen and Kai Zehmisch},
  journal= {arXiv preprint arXiv:1309.4982},
  year   = {2017}
}

Comments

6 pages

R2 v1 2026-06-22T01:30:18.371Z